Potential and electric field distribution in a ceramic disc insulator string with faulty insulators

Ceramic/Porcelain suspension disc insulators are widely used in power systems to provide electrical insulation and mechanically support for high-voltage transmission lines. These insulators are subjected to a variety of stresses, including mechanical, electrical and environmental. These stresses act in unison. The exact nature and magnitude of these stresses vary significantly and depends on insulator design, application and its location. Due to various reasons the insulator disc can lose its electrical insulation properties without any noticeable mechanical failure. Such a condition while difficult to recognize, can enhance the stress on remaining healthy insulator discs in the string further may lead to a flashover. To understand the stress enhancement due to faulty discs in a string, attempt has been made to simulate the potential and electric field profiles for various disc insulators presently used in the country. The results of potential and electric filed stress obtained for normal and strings with faulty insulator discs are presented.

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Branes and supersymmetric quantum field theories

Since the discovery of D-branes as non-perturbative, dynamic objects in string theory, various configurations of branes in type IIA/B string theory and M-theory have been considered to study their low-energy dynamics described by supersymmetric quantum field theories.

One example of such a construction is based on the description of Seiberg-Witten curves of four-dimensional N = 2 supersymmetric gauge theories as branes in type IIA string theory and M-theory. This enables us to study the gauge theories in strongly-coupled regimes. Spectral networks are another tool for utilizing branes to study non-perturbative regimes of two- and four-dimensional supersymmetric theories. Using spectral networks of a Seiberg-Witten theory we can find its BPS spectrum, which is protected from quantum corrections by supersymmetry, and also the BPS spectrum of a related two-dimensional N = (2,2) theory whose (twisted) superpotential is determined by the Seiberg-Witten curve. When we don’t know the perturbative description of such a theory, its spectrum obtained via spectral networks is a useful piece of information. In this thesis we illustrate these ideas with examples of the use of Seiberg-Witten curves and spectral networks to understand various two- and four-dimensional supersymmetric theories.

First, we examine how the geometry of a Seiberg-Witten curve serves as a useful tool for identifying various limits of the parameters of the Seiberg-Witten theory, including Argyres-Seiberg duality and Argyres-Douglas fixed points. Next, we consider the low-energy limit of a two-dimensional N = (2, 2) supersymmetric theory from an M-theory brane configuration whose (twisted) superpotential is determined by the geometry of the branes. We show that, when the two-dimensional theory flows to its infra-red fixed point, particular cases realize Kazama-Suzuki coset models. We also study the BPS spectrum of an Argyres-Douglas type superconformal field theory on the Coulomb branch by using its spectral networks. We provide strong evidence of the equivalence of superconformal field theories from different string-theoretic constructions by comparing their BPS spectra.

Dynamical scattering models in optomechanics: Going beyond the 'coupled cavities' model

Recently [A. Xuereb, et al., Phys. Rev. Lett. 105, 013602 (2010)], we calculated the radiation field and the optical forces acting on a moving object inside a general one-dimensional configuration of immobile optical elements. In this article we analyse the forces acting on a semi-transparent mirror in the 'membrane-in-the-middle' configuration and compare the results obtained from solving scattering model to those from the coupled cavities model that is often used in cavity optomechanical system. We highlight the departure of this model from the more exact scattering theory when the reflectivity of the moving element drops below about 50%.

Hierarchical Bayesian models in ecology: Reconstructing species interaction networks from non-homogeneous species abundance data

The relationships among organisms and their surroundings can be of immense complexity. To describe and understand an ecosystem as a tangled bank, multiple ways of interaction and their effects have to be considered, such as predation, competition, mutualism and facilitation. Understanding the resulting interaction networks is a challenge in changing environments, e.g. to predict knock-on effects of invasive species and to understand how climate change impacts biodiversity. The elucidation of complex ecological systems with their interactions will benefit enormously from the development of new machine learning tools that aim to infer the structure of interaction networks from field data. In the present study, we propose a novel Bayesian regression and multiple changepoint model (BRAM) for reconstructing species interaction networks from observed species distributions. The model has been devised to allow robust inference in the presence of spatial autocorrelation and distributional heterogeneity. We have evaluated the model on simulated data that combines a trophic niche model with a stochastic population model on a 2-dimensional lattice, and we have compared the performance of our model with L1-penalized sparse regression (LASSO) and non-linear Bayesian networks with the BDe scoring scheme. In addition, we have applied our method to plant ground coverage data from the western shore of the Outer Hebrides with the objective to infer the ecological interactions. (C) 2012 Elsevier B.V. All rights reserved.

Evidence of aging in spin glass mean-field models

We study numerically the out-of-equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models. This suggests that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.

Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.

Interface dynamics in planar neural field models

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.

Quantum states, thermodynamic limits, and entropy in M theory

We discuss the matching of the BPS part of the spectrum for a (super) membrane, which gives the possibility of getting the membrane's results via string calculations. In the small coupling limit of M theory the entropy of the system coincides with the standard entropy of type IIB string theory (including the logarithmic correction term). The thermodynamic behavior at a large coupling constant is computed by considering M theory on a manifold with a topology T-2 x R-9. We argue that the finite temperature partition functions (brane Laurent series for p not equal 1) associated with the BPS p-brane spectrum can be analytically continued to well-defined functionals. It means that a finite temperature can be introduced in brane theory, which behaves like finite temperature field theory. In the limit p --> 0 (point particle limit) it gives rise to the standard behavior of thermodynamic quantities.

Entropy and thermodynamic limits in M-theory

The matching of the BPS part of the (super) membrane's spectrum enables one to obtain membrane's results via string calculations. We compute the thermodynamic behavior at large coupling constant by considering M-theory on a manifold with topology T-2 X R-9. In the small coupling limit of M-theory the entropy coincides with the standard entropy of type IIB strings. We claim that the finite temperature partition functions associated with BPS p-brane spectrum can be analytically continued to well-defined functionals. This means that finite temperature can be introduced in brane theory. For the point particle limit (p --> 0) the entropy has the standard behavior of thermodynamic quantities.

Alternative string theory in twistor space for N=4 super-Yang-Mills theory

In this Letter, an alternative string theory in twistor space is proposed for describing perturbative N=4 super-Yang-Mills theory. Like the recent proposal of Witten, this string theory uses twistor worldsheet variables and has manifest spacetime superconformal invariance. However, in this proposal, tree-level super-Yang-Mills amplitudes come from open string tree amplitudes as opposed to coming from D-instanton contributions.

Self-dual super-Yang-Mills as a string theory in (x, 0) space

Different string theories in twistor space have recently been proposed for describing N = 4 super-Yang-Mills. In this paper, a string theory in (x, theta) space is constructed for self-dual N = 4 super-Yang-Mills. It is hoped that these results will be useful for understanding the twistor-string proposals and their possible relation with the pure spinor formalism of the d = 10 superstring.

Class of self-dual models in three dimensions

In the present paper we introduce a hierarchical class of self-dual models in three dimensions, inspired in the original self-dual theory of Towsend-Pilch-Nieuwenhuizen. The basic strategy is to explore the powerful property of the duality transformations in order to generate a new field. The generalized propagator can be written in terms of the primitive one (first order), and also the respective order and disorder correlation functions. Some conclusions about the charge screening and magnetic flux were established. ©1999 The American Physical Society.

Self-dual super-Yang-Mills as a string theory in (x, θ) space

Different string theories in twistor space have recently been proposed for describing N = 4 super-Yang-Mills. In this paper, a string theory in (x, θ) space is constructed for self-dual N = 4 super-Yang-Mills. It is hoped that these results will be useful for understanding the twistor-string proposals and their possible relation with the pure spinor formalism of the D = 10 superstring. © SISSA/ISAS 2004.